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Message: <blockquote data-quote="DracoSuave" data-source="post: 5701709" data-attributes="member: 71571">Incredibly intuitive, and there are many games that use it.However, instead of rating stats from 8-20, they rate them from 1-5 (as an example) because the amount of variance caused by a stat point is so much more.The thing with d20 math is without the flattening of the ability score's contribution, if you ever have an opposed check, a difference of, say, 4, isn't a 20% variable of success.  The probability actually works out quiiiiite different, because you're dealing with a bell curve and not a line.So, in this instance, 20% of all attempts the one with the advantage wins, without contest from the disadvantaged.  As well, in 20% of all attempts, the one with the disadvantage loses without contest from the advantaged.  4% of the time, both will roll in their no contest range.  This ends up that 36% of the time, the advantaged will win with no contest.The rest of it is a 50/50 split (provided ties don't go to the advantaged) so a four point bonus in opposed checks (such as initiative) actually leads to 68% chance of victory for the one with the advantage.  There's a reason why people with improved initiative seem to go first a lot more often 20% of the time.The interesting thing is that 3rd and 4th edition didn't flatten the math... they steepened it, allowing bonuses at 12, rather than at 15, and allowing those bonuses to go up to 4, rather than the usual 2.  (Percentile Strength is an oddity)</blockquote>

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